Postseismic relaxation associated with transient creep rheology

Abstract

Perfettini and Avouac (2004) postulated that both the aftershock rate (assumed proportional to the local stressing rate) and the postseismic relaxation are driven by the loading imposed by postseismic slip on the brittle creep fault zone (BCFZ), the downdip extension of the fault zone below the coseismic rupture. I explore the consequences of that hypothesis for a long, strike‐slip fault in the case where the BCFZ rheology is compatible with ordinary transient creep (creep strain proportional to loge(1 + t/τ2)). Because the important relaxation occurs near the bottom of the coseismic rupture, I calculate the postearthquake response with a model in which the BCFZ is represented by a viscoelastic half‐space below the coseismic rupture. I find that both the predicted postseismic relaxation and the cumulative number of aftershocks can be approximated by the same temporal dependence NMO(t) = aMO(1−(1 + t/τ)1−p)/(p − 1), where t is the time after the earthquake and aMO, τ, and p are the constants chosen to fit either data set. Notice that dNMO(t)/dt = (aMO/τ)/(1 + t/τ)p is the modified Omori law used to describe the rate of aftershock occurrence. Thus, the modified Omori law can be understood as a consequence of the Perfettini–Avouac hypothesis (aftershocks driven by slip on the BCFZ) and a BCFZ rheology compatible with ordinary transient creep. Moreover, the temporal dependence NMO(t) has been shown to fit postseismic surface deformation following at least 9 earthquakes. I also show that the conventional, one‐dimensional, spring‐block model of a BFCZ with a rheology compatible with ordinary transient creep leads to the same temporal dependence (NMO(t)).